My son has parolee I94 card from July, we went to SSN office on 8/29 to apply SSN for him who is 12 years old. I did not realize that my hu*****and renewed his H-1B in May and got approved on 8/25, so technically my son is in H-4 status when we went to the local office.
I think either 485 receipt or stamped AP is indeed needed when applying, since the officer mentioned that after key in info on I94 card, the system still asks for more information, eventually I showed her both the stamped AP and 485 notice and she picked some info from the form and had it processed, maybe the A# is needed, I am not sure. received SSN card for my son today, just in time to file 1040x for tax credit.
Thanks again, pjiang and xiaobaitu, I only thought of applying SSN for my son after we did not receive tax credit for him, but I did not think applying SSN was possible w/o EAD for him, finally I came across the article from pjiang and xiaobaitu that we can apply using parolee I-94.